How much energy is stored up high.
Lift a mass to a height and it stores gravitational potential energy, PE = m x g x h. Enter any two of mass, height, and energy and this solves the third, then shows the speed it would reach if you dropped it.
The setup
What these numbers mean
Energy stored as you go higher
Potential energy vs height at this mass
If you dropped it
Energy and impact speed by height
Same mass and gravity, dropped from each height with no air resistance. Impact speed is v = sqrt(2 x g x h) and impact energy equals the stored PE.
| Height | PE (J) | PE (report unit) | Drop speed (m/s) | Drop speed (mph) |
|---|
Potential energy, explained
The Reference Point Matters
Potential energy is always relative to a chosen reference level (usually the ground). The same object 10 m above the ground has different PE if you reference from the ground vs from the rooftop. Pick a reference and stick with it for any analysis, what matters physically is the CHANGE in PE between two points, not the absolute value at one point.
Conversion to Kinetic Energy
When the object falls (and air resistance is ignored), PE converts to kinetic energy. At the bottom, KE = PE at the top, so the final velocity is v = sqrt(2gh). This lets you predict impact speeds: a 1 kg object dropped from 10 m hits at 14 m/s carrying 98 J of KE, exactly the PE it started with.
Gravity on Other Planets
Mercury: 3.7 m/s². Venus: 8.87. Mars: 3.71. Jupiter: 24.79. Saturn: 10.44. Uranus: 8.69. Neptune: 11.15. Moon: 1.62. Adjust the gravity field in the calculator for non-Earth scenarios. A 100 kg astronaut at 5 m altitude on the Moon has only 810 J of PE vs 4,905 J on Earth.
Beyond Gravitational PE
This calculator handles gravitational potential energy specifically. Other forms exist: elastic PE (spring stretched, PE = 0.5kx²), chemical PE (bonds in molecules), electric PE (charges in a field). The general principle is the same: PE is energy stored due to position or configuration that can be released as kinetic energy.
Common questions
What is the gravity value on other planets?
Mercury: 3.7, Venus: 8.87, Mars: 3.71, Jupiter: 24.79, Saturn: 10.44, Uranus: 8.69, Neptune: 11.15, Moon: 1.62 (all m/s²).
Why does the reference point matter?
Physics only cares about the CHANGE in PE between two points, not absolute values. The reference is your choice, usually ground level, but you need to be consistent within one calculation.
What's the relationship between PE and KE?
In a closed system without friction, total energy (PE + KE) is conserved. As an object falls, PE decreases and KE increases by equal amounts. At the bottom of a free fall, KE = original PE.
Does this account for air resistance?
No, this assumes no air resistance. Real falling objects experience drag, so impact KE is less than initial PE. The difference goes to heating the air through friction.
Can PE be negative?
Yes, if the object is below your chosen reference level. The sign indicates position relative to reference, not anything physical. A ball below ground level has negative PE relative to ground.
Idealized physics for learning and planning. Real drops lose energy to air resistance, so measured impact speed and energy are lower than these frictionless values. Gravity varies slightly with altitude and latitude.